给定直径和阶的具有最大Wiener指标的单圈图

The Maximal Wiener Index of UnicyclicGraph with Given Diameter and Order

摘要: 图的Wiener指标是图论中研究的比较深刻的拓扑指标之一，结果很丰富，同时也有许多有趣的问题没有被解决，尽管这些问题很容易表述也很容易被理解。在这篇文章中，我们着重研究由DelaVina和Waller提出的一个猜想，即：点数是2d + 1，直径为d的图的Wiener指标都不超过点数是2d + 1的圈的。本文证明了该猜想对于单圈且圈外顶点数不多的图是正确的。

Abstract: The Wiener index of a graph is one of the most very well-researched topological indices, i.e. graph theoretic invariants of molecular graphs. Some interesting questions remain largely unsolved de-spite being easy to state and comprehend. In this paper, we investigate a conjecture proposed by DelaVina and Waller, namely, the graphs of order 2d + 1 and diameter d have Wiener index less or equal than the cycle of order 2d + 1. In this paper, we proved that this conjecture is true for unicyclic graphs with vertices outside of the cycle not too many.